All Questions
12 questions
0votes
0answers
70views
Determine 3-point function by conformal symmetry
I already posted question to math stack but I haven't yet gotten answer. So, I ask here. I'd like to know a form of functions (called 3-point function) that have symmetry under some transformation. ...
1vote
0answers
102views
Functional derivative of a Green function
I'm trying to prove that, given the Hamiltonian $\hat{H} + \int d\mathbf{x} \hat{n}(\mathbf{x})\varphi(\mathbf{x}, t)$, where $\varphi(\mathbf{x}, t)$ is some external field and $\hat{S}$ the ...
- 173
1vote
1answer
175views
Calculation of $ \gamma(\lambda) $ in massless renormalizable scalar field theory
In Peskin & Schroeder p.413 and 414, the Callan-Symanzik equation for a 2-point Green's function is used to calculate $ \gamma(\lambda) $ for a massless renormalizable scalar field theory. The two-...
- 1,115
0votes
1answer
77views
Finding scalar propagators in QFT for specific spacetime dimension $d$ and mass $m$
I need to understand how in practice one finds propagators for given $d$ and $m$ in quantum field theory. I can write down the theory provided for it but I don't know how to use it. We will compute ...
- 1
3votes
1answer
819views
Propagator for a massless scalar field in $d$-dimensional spacetime [closed]
I'm trying to show that for a free massless scalar field, the 2-point correlation function in $d$-dimensional spacetime has the following form: $$<\phi(x)\phi(y)> = \int \frac{d^d{p}}{(2\pi)^d}\...
1vote
0answers
120views
Perturbation to two-point correlation function for the anharmonic oscillator [closed]
I am trying to answer a question regarding the computation of the first-order correction to the two-point correlation function for the anharmonic oscillator with Lagrangian: $$ L = \frac{m}{2} \dot x^...
2votes
1answer
763views
Help with Wick's theorem in a $\phi^4$ QFT
QFT noob here. I am currently working out the momentum space two-point function for a $\phi^4$ qft in Euclidean space time, and considering the $\lambda^1$ order contribution, I am encountering a ...
1vote
2answers
189views
Relation between Green’s functions and connected Green’s functions [closed]
I attempt to understand the $0$-dimensional QFT from these QFT lecture notes by Ronald Kleiss from 2019. The author defines the generating function $Z(J)$ and its logarithm in the following way. $$Z(J)...
- 3,083
5votes
2answers
2kviews
Callan-Symanzik Equation
In the book An Introduction to Quantum Field Theory by Michael E. Peskin and Daniel V. Schroeder they derive the Callan-Symanzik equation for the two-point function \begin{equation} \left[M\frac{\...
- 525
2votes
1answer
589views
Commutator of massless scalar field
Hello I'm trying to calculate $\langle 0|[\phi(x),\phi(0)]|0\rangle$ where $\phi (x)$ is a free massless scalar field. I've computed $$\langle 0|\phi (x) \phi (0)|0\rangle = \frac{1}{4\pi^2}\frac{1}{(...
- 2,835
12votes
1answer
3kviews
How do I Derive the Green's Function for $-\nabla^2 + m^2$ in $d$ dimensions?
What is the solution to this equation in $d$ dimensions: $$(-\nabla_d^2 + m^2)G(\mathbf{x}, \mathbf{x}') = A \delta(\mathbf{x} - \mathbf{x}'),$$ with the boundary condition that $\lim_{|\mathbf{x} - \...
- 22.9k
5votes
0answers
2kviews
Two-point function of a free massless scalar field in Euclidean space-time
Let $\phi(x)$ be a free massless scalar field on $d$-dimesnional space-time with Euclidean metric. I am interested in the operator formalism, i.e. $\phi(x)$ is an operator satisfying $\Delta \phi=0$ ...
- 2,339
